Math Homework Help?

A landscape architect is designing a triangular garden to fit in the corner of a lot. The corner of the lot forms an angle of 70 degrees, and the sides of the garden including this angle are to be 11 feet and 13 feet, respectively. Find, to the nearest integer, the number of square feet in the area of the garden.

Math Homework Help?
First, I'd use the Law of Cosines to find the length of the missing side:



b^2 = a^2 + c^2 - 2ac(cos B)



b^2 = 169 + 121 - 286cos(70).



b^2 = 192.1822.



b = 13.8630.



Now use this length, since you know all the side lengths now, with Heron's Formula to find the area of the triangle.



Heron's Formula: Area = sqrt(s(s-a)(s-b)(s-c)) where s = semiperimeter of the triangle.



s = (13.86 + 11 + 13)/2 = 18.93.



Area = sqrt((18.93)(5.07)(7.93)(5.93)) = 67.18 square feet.



-John
Reply:In this case, you can calculate the area of the triangle using,

(1/2) (11)(13)sin(70)

=(1/2)(143)(0.9397)=67.19 sq ft



The area of a triangle is also the product of two sides times the sine of the angle included between them.